Skip to main content
Log in

Point Estimation for the Ratio of Medians of Two Independent Log-Normal Distributions

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

We focus on the normal approximation for point estimation of the ratios of medians of two independent, log-normal distributions. We investigate its performance in terms of bias, variance, and mean square error, using Monte Carlo simulations. The results show that the normal approximation, which is relatively simple, provides a reliable result. The normal approximation approaches could be recommended on the basis of the specific values of the parameters and/or sample sizes. The point estimation is illustrated using real data examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

REFERENCES

  1. C. E. Land, ‘‘An evaluation of approximate confidence interval estimation methods for lognormal means,’’ Technometrics 14, 145–158 (1972).

    Article  Google Scholar 

  2. J. E. Angus, ‘‘Inferences on the lognormal mean for complete samples,’’ Commun. Stat.-Simul. Comput. 17, 1307–1331 (1988).

    Article  MathSciNet  Google Scholar 

  3. J. E. Angus, ‘‘Bootstrap one-sided confidence intervals for the lognormal mean,’’ Statistician 43, 395–401 (1994).

    Article  Google Scholar 

  4. X. H. Zhou and S. Gao, ‘‘Confidence intervals for the lognormal mean,’’ Stat. Med. 16, 783–790 (1997).

    Article  Google Scholar 

  5. D. J. Taylor, L. L. Kupper, and K. E. Muller, ‘‘Improved approximate confidence intervals for the mean of a lognormal random variable,’’ Stat. Med. 21, 1443–1459 (2002).

    Article  Google Scholar 

  6. J. Wu, A. C. M. Wong, and G. Jiang, ‘‘Likelihood-based confidence intervals for a log-normal mean,’’ Stat. Med. 22, 1849–1860 (2003).

    Article  Google Scholar 

  7. N. Smithpreecha, S. Niwitpong, and S. Niwitpong, ‘‘Confidence intervals for common mean of lognormal distributions,’’ in Proceedings of the International Econometric Conference of Vietnam (Springer, Cham, 2018), pp. 276–289.

  8. X.-H. Zhou and W. Tu, ‘‘Interval estimation for the ratio in means of log-normally distributed medical costs with zero values,’’ Comput. Stat. Data Anal. 35, 201–210 (2000).

    Article  MathSciNet  Google Scholar 

  9. J. Wu, G. Jiang, A. C. M. Wong, and X. Sun, ‘‘Likelihood analysis for the ratio of means of two independent log-normal distributions,’’ Biometrics 58, 463–469 (2002).

    Article  MathSciNet  Google Scholar 

  10. K. Krishnamoorthy and T. Mathew, ‘‘Inferences on the means of lognormal distributions using generalized \(p\)-values and generalized confidence intervals,’’ J. Stat. Plan. Inf. 115, 103–120 (2003).

    Article  Google Scholar 

  11. P. Gill, ‘‘Small-sample inference for the comparison of means of log-normal distributions,’’ Biometrics 60, 525–527 (2004).

    Article  MathSciNet  Google Scholar 

  12. Y.-H. Chen and X.-H. Zhou, ‘‘Interval estimates for the ratio and difference of two log-normal means,’’ Stat. Med. 25, 4099–4113 (2006).

    Article  MathSciNet  Google Scholar 

  13. K. Cimermanová, ‘‘Estimation of confidence intervals for the log-normal means and for the ratio and the difference of log-normal means with application of breath analysis,’’ Meas. Sci. Rev. 7 (4), 31–36 (2007).

    Google Scholar 

  14. G. Y. Zou, J. Taleban, and C.-Y. Huo, ‘‘Confidence interval estimation for lognormal data with application to health economics,’’ Comput. Stat. Data Anal. 53, 3755–3764 (2009).

    Article  MathSciNet  Google Scholar 

  15. J. Poirier, G. Y. Zou, and J. Koval, ‘‘Confidence intervals for a difference between lognormal means in cluster randomization trials,’’ Stat. Methods Med. Res. 26, 598–614 (2017).

    Article  MathSciNet  Google Scholar 

  16. S. G. Kang, W. D. Lee, and Y. Kim, ‘‘Objective Bayesian analysis using modified profile likelihood for the ratio of two log-normal means,’’ J. Korean Stat. Soc., 1–22 (2020).

  17. A. Baklizi and M. Ebrahem, ‘‘Interval estimation of common lognormal mean of several populations,’’ J. Probab. Stat. Sci. 3(1), 1–16 (2005).

    Google Scholar 

  18. L. Tian and J. Wu, ‘‘Inferences on the common mean of several log-normal populations: The generalized variable approach,’’ Biometr. J. 49, 944–951 (2007).

    Article  MathSciNet  Google Scholar 

  19. J. Behboodian and A. Jafari, ‘‘Generalized inference for the common mean of several lognormal populations,’’ J. Stat. Theory Appl. 5, 240–259 (2006).

    MathSciNet  Google Scholar 

  20. S. H. Lin and R. S. Wang, ‘‘Modified method on the means for several log-normal distributions,’’ J. Appl. Stat. 40, 194–208 (2013).

    Article  MathSciNet  Google Scholar 

  21. A. Malekzadeh and M. Kharrati-Kopaei, ‘‘Inferences on the common mean of several heterogeneous log-normal distributions,’’ J. Appl. Stat. 46, 1066–1083 (2019).

    Article  MathSciNet  Google Scholar 

  22. A. Zellner, ‘‘Bayesian and non-Bayesian analysis of the log-normal distribution and log-normal regression,’’ J. Am. Stat. Assoc. 66 (334), 327–330 (1971).

    Article  MathSciNet  Google Scholar 

  23. K. A. Rao and J. G. D’Cunha, ‘‘Bayesian inference for median of the lognormal distribution,’’ J. Mod. Appl. Stat. Methods 15, 526–535 (2016).

    Article  Google Scholar 

  24. G. Y. Zou, ‘‘On the estimation of additive interaction using the four-by-two table and beyond,’’ Am. J. Epidemiol. 168, 212–224 (2008).

    Article  Google Scholar 

  25. G. Y. Zou and A. Donner, ‘‘Construction of confidence limits about effect measures: A general approach,’’ Stat. Med. 27, 1693–1702 (2008).

    Article  MathSciNet  Google Scholar 

  26. S. Weerahandi, ‘‘Generalized confidence intervals,’’ J. Am. Stat. Assoc. 88, 899–905 (1993).

    Article  MathSciNet  Google Scholar 

Download references

Funding

The third author’s research was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project no. 1.13556.2019/13.1.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Lapasrada Singhasomboon, Wararit Panichkitkosolkul or Andrei Volodin.

Additional information

(Submitted byWinai Bodhisuwan)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singhasomboon, L., Panichkitkosolkul, W. & Volodin, A. Point Estimation for the Ratio of Medians of Two Independent Log-Normal Distributions. Lobachevskii J Math 42, 415–425 (2021). https://doi.org/10.1134/S1995080221020177

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080221020177

Keywords:

Navigation